Fluorescence correlation spectroscopy (FCS) is a standard tool for studying diffusion of molecules in solution, but is limited to low analyte concentrations, in the range between 10 pM and 1 nM. Such concentration limitations can be overcome by using a plasmonic nanoantenna which confines the electric field of excitation light into a tiny volume near its surface and thereby reduces the effective excitation volume by several orders of magnitude. Here we demonstrate successful FCS measurements on a 1 μM solution of crystal violet (CV) dye in glycerol using a gold nanorod antenna. Our correlation analysis yields two components: (i) a slow component with correlation time of about 100 ms, which is attributed to sticking and bleaching of the dye, and (ii) a fast component of about 1 ms, which could arise from dye diffusion through the near-field of the nanorod and/or from blinking due to intersystem crossing or photochemistry.